Find all numbers c that satisfy the conclusion of Rolle's Theorem for the following function.

Question

If there are multiple values, separate them with commas; enter N if there are no such values.
f(x)= x^2-10x+3, [0,10]

Answer 1

Rolle's Theorem needs f(0) = f(10).
This is true.

So, we know that there is a c such that f'(c) = 0, where 0 <= c <= 10.

f'(x) = 2x-10
So, if f'(c) = 0, c=5.
c is indeed in the interval.